Furthermore, as shown in FIG. 5, a duty cycle D of the LPWM signal is given by:
                              D          =                                    1              -                                                2                  ×                  T                  ⁢                                                                          ⁢                  1                                T                                      =                                          1                -                                                      2                    ×                    T                    ⁢                                                                                  ⁢                    1                                                        (                                          1                                              2                        ×                        f                        ⁢                                                                                                  ⁢                        1                                                              )                                                              =                              1                -                                  4                  ×                  f                  ⁢                                                                          ⁢                  1                  ×                  T                  ⁢                                                                          ⁢                  1                                                                    ,                            (        5        )            where T is a period of the LPWM signal. Since the product of f1 and T1 is a constant value, the duty cycle D of the LPWM signal is also substantially constant regardless of the amplitude and/or frequency variations in the AC input voltage VIN. In one embodiment, the duty cycle of the LPMW signal from the LPWM generator 430 is determined by the resistors 311, 313, 315 and 317. By changing the resistance of these resistors, the duty cycle of the LPWM signal can be adjusted to adapt to various applications, in one embodiment.
The waveform 509 in FIG. 5 represents an example of an LPWM signal generated by the LPWM generator 430. The waveform 510 in FIG. 5 represents an example of a dimming control signal DIM output from the AND gate 409. When the signal VSIN is less than the signal VDC, the LPWM signal is logic low (OFF period). During an OFF period, the dimming control signal DIM output is logic low such that the control switch 411 is switched off. There is no current flowing through the LED string 340 during the OFF period. When the signal VSIN is greater than the signal VDC, the LPWM signal is logic high (ON period). During an ON period, a feedback signal FB indicative of a current through the LED string 340 is compared to the predetermined reference signal VREF. The dimming control signal DIM is determined by a pulse signal generated by the frequency generator 440 and a comparison result of the feedback signal FB and the predetermined reference signal VREF. By way of example, the pulse signal from the frequency generator 440 can have a frequency between approximately 300 KHz and 2.5 MHz. Controlled by the dimming control signal DIM, the control switch 411 can be switched on and off alternately to regulate the LED current flowing through the LED string 340.
However, in the circuit 100 as shown in FIG. 1, only when the AC input voltage VIN is higher than the voltage across the electrolytic capacitor 105, the input current IIN conducts through the rectifier 103. Consequently, the input current IIN represents a pulsating current waveform, which results in a poor power factor, e.g., 0.6. Additionally, the life time or mean time between failures (MTBF) of the electrolytic capacitor 105 is much shorter than other elements of LED driving systems. As such, the electrolytic capacitor 105 dominates the life time of such LED driving systems and therefore impairs the advantage of long operating life of LED light sources.